Tests for Normal distribution

Tests available in MedCalc

MedCalc offers the following tests for Normal distribution:

The Shapiro-Wilk test (Shapiro & Wilk, 1965; Royston, 1995) and the Shapiro-Francia test (Shapiro & Francia, 1972; Royston, 1993a) calculate a W and W' statistic, respectively, that tests whether a random sample comes from a Normal distribution. Small values of W or W' are evidence of departure from normality. The Shapiro-Wilk W statistic can only be computed when sample size is between 3 and 5000 (inclusive) (Royston, 1995), the Shapiro-Francia W' statistic can be computed when sample size ranges from 5 to 5000 (Royston, 1993a & 1993b).

The D'Agostino-Pearson test (Sheskin, 2011) computes a single P-value for the combination of the coefficients of Skewness and Kurtosis.

The Kolmogorov-Smirnov test (Neter et al., 1988) with Lilliefors significance correction (Dallal & Wilkinson, 1986) is based on the greatest discrepancy between the sample cumulative distribution and the Normal cumulative distribution.

The Chi-squared goodness-of-fit test is applied to binned data (the data are put into classes) (Snedecor & Cochran, 1989) and requires a
larger sample size than the other tests.

Results

The result of this test is expressed as 'accept Normality' or 'reject Normality', with P value.

If P is higher than 0.05, it may be assumed that the data have a Normal distribution and the conclusion accept Normality is displayed.

If P is less than 0.05, then the hypothesis that the distribution of the observations in the sample is Normal, should be rejected, and the conclusion reject Normality is displayed.